Problem: Jessica is 2 times as old as Umaima. Twelve years ago, Jessica was 6 times as old as Umaima. How old is Umaima now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Umaima. Let Jessica's current age be $j$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $j = 2u$ Twelve years ago, Jessica was $j - 12$ years old, and Umaima was $u - 12$ years old. The information in the second sentence can be expressed in the following equation: $j - 12 = 6(u - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 2u$ . Substituting this into our second equation, we get: $2u$ $-$ $12 = 6(u - 12)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $2 u - 12 = 6 u - 72$ Solving for $u$ , we get: $4 u = 60.$ $u = 15$.